2. The line graph L(G) of a graph G has a vertext for each edge of G, and two of these vertices are adjacent if and only if the corresponding edges in G have a vertex in common. (a) Find L(G) for the graph in question 1. (b) Prove that if the simple graph G has an Euler circuit, then its line graph L(G) also contains an Euler circuit. 1. An open Eulerian path is a path that uses every edge in the graph, but does not end where it begins. Construct an open Eulerian path in the following graph. a g d